This morning, Rachel Monahan reported in the New York Daily News that two of the three New York City schools that piloted the “School of One” decided to drop the program. After a great deal of expenditure and hype, the School of One didn’t show better results on the state math tests than regular math classes.
I am not surprised by this report. The School of One (which I discuss in the eighth chapter of my book) assumes that mathematics consists of a progression of skills. Its proprietary software program generates a daily “playlist” for each student and lesson plans for the teachers. Students enter the classroom, view their playlist, and go to their appointed station. On a given day, a student might play a video game, work in a small group, receive direct instruction from a teacher, or engage in some combination of these activities. Teachers might spend fifteen minutes with one group, a few minutes here and there with individuals, and another fifteen minutes with another group. The students take frequent multiple-choice quizzes, which help to determine their activities and grouping. Supposedly, by working at their own pace in their own preferred style, students will make great progress.
But mathematics is not an amusement park. It is about recognizing patterns and seeing problems in more than one way. It requires imagination as well as precision. In the best math classes, students learn to struggle with problems that at first seem daunting (but for which they are adequately prepared). They try this and that, seeming to get nowhere, and then suddenly they see it. In a flash, it is all clear—and the solution sheds light on problems from earlier lessons and problems still to come.
Students cannot rely on such flashes of insight, of course. After solving a difficult problem, they must practice solving similar problems until they come easily. Then they continue on to the next challenge, which often arises out of the problems they have solved. A good math curriculum has a clear, logical progression but also moves back and forth and outward. Over time, as students advance and gain knowledge and experience, they develop what Alfred North Whitehead called “that eye for the whole chess-board, for the bearing of one set of ideas on another.”
Personalized, computerized instruction doesn’t do justice to such a curriculum; even precocious students need guidance through the challenges. It is the teacher who knows how to pose a problem in different ways and to draw more than the obvious conclusions from it. It is the teacher who can glean where a student is going wrong and guide him back on track. Such teaching takes time. A class can easily spend an entire lesson on a single theorem or concept, and the students learn from each other’s efforts.
What happens when the lesson is fragmented, when students go off into their various groups and corners to play a game or work on an activity? Well, in many cases both the students and the mathematics itself are shortchanged. The students may make progress with problems of a basic sort (like those that appear in summer math workbooks) but will need the teacher for the trickier and subtler points. Also, flitting from activity to activity isn’t always helpful; mathematics requires focus and doggedness. (Yes, sometimes the solution comes to you after you walk away—but those hours of puzzling and pondering help to bring this about.)
So why has the the School of One enjoyed such hype? Not only are there powerful political and commercial entities behind it, but it appears to address a real problem. Today’s classrooms have a wide range of levels; the advanced and struggling students study together. Since tracking is not an option (especially at the elementary and middle school levels), the teacher is expected to accommodate all levels at once. Given that state of things, a personalized learning system (aided by software) sounds like a crystal palace of sorts. To some, it is the future.
But to paraphrase Fyodor Dostoevsky’s Underground Man, if it is raining and I crawl into a hen-house in order to stay dry, I will not call it a palace out of gratitude. It is still a hen-house. Something analogous holds true for the School of One. It is a makeshift solution, and an expensive one at that.
What can we do instead of expanding the School of One? We could adopt strong math curricula that give students a foundation in the early grades. We could allow for certain kinds of flexible tracking—so that, for instance, a fifth-grade student could take math with sixth graders if she were prepared (but would take other classes with her fifth-grade classmates). We could have public lectures, seminars, and workshops on mathematics, so that parents, teachers, and others could grapple with math problems together. We could identify first-rate math textbooks, possibly translating a few from other languages, so that teachers did not have to scramble for appropriate resources. All of this would be far less expensive—and far truer to the purpose of teaching math—than the School of One.
Take Away the Takeaway 
ashanam
/ September 8, 2012I like what you what you have to say about math instruction. However, I don’t think tracking is really the answer. It may work well for the kids in the middle, but the children who struggle usually struggle not just because they are bad at math but because they have difficulty with behavioral, social, and emotional issues that impact learning. When these students are grouped together, they lose out on having positive role models and do even worse.
Diana Senechal
/ September 8, 2012I, too, am ambivalent about tracking–when I said “flexible tracking,” I was thinking of a system that would allow for some movement from one track to another. That said, I see problems with that as well.
In an ideal world, every student would be in a class with students slightly above his or her level. Of course that is logistically impossible.
I see your point that the struggling students need positive role models. But advanced kids can easily get restless and stop being good role models when they aren’t being challenged. How many stories have I heard about advanced kids who were grateful to be allowed to sit in the back of the room and read? Many of them had to wait until high school for an intellectually stimulating and substantial class.
ashanam
/ September 8, 2012Unfortunately, the low students usually remain in the lowest track whenever there is tracking–and often they remain together for most of their school years. They do improve, but rarely more than everyone else.
I think it is possible to reach a fairly wide range of students in a regular classroom, provided you don’t have a lot of students with different, extremely intense needs. (My newcomer this year should probably not be in a class full of students with learning disabilities or that have low academic skills and behavior problems.)
Gifted students sometimes do well in elementary school when they are clustered–so they are tracked, but no one else is. I had a cluster last year (coincidentally, not intentionally), and I think the whole class enjoyed them and benefited from their being there.
Profoundly gifted students do need something different, but there are so few of them they can be dealt with on a case-by-case basis. I let one student program computers all through math class a few years ago. I really don’t expect to have another student like him again.
It’s really the average or slightly above average students that do well mainly because they work hard that make the best role models.